A computationally efficient explicit-implicit FEM in parallel manner to analyze the response of three-dimensional soil-structure system subjected to seismic wave is presented. The unbounded soil is modelled by lumped-mass explicit finite element method and viscoelastic artificial boundary, the structure is analysed through implicit finite element method, and response of the rigid foundation is calculated through explicit time integration scheme. The different time steps can be chosen for the explicit and implicit integration scheme, which can greatly improve the efficiency. The synchronous and asynchronous parallel algorithms using MPI are proposed for the soil-structure interaction analysis. The codes for this method are programmed. Example for seismic response analysis of a nuclear plant is given, which validates the feasibilty and efficiency of the proposed method.